A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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91 views

How to derive an option price for an asset with these dynamics?

Assuming my underline asset price follows the process: $$d\ln (F_{t,T})=-(1/2)\sigma ^2e^{-2\lambda(T-t)}dt+\sigma e^{-\lambda(T-t)}dB_t $$ How should I derive an option price formula?
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3answers
113 views

What is the theoretical expected growth in an option's value over a given period of time?

Say an option with five years left before maturity has a value of $x$ today. Theoretically, under the B/S framework, what is its expected value in five years (upon maturity)? Do we assume it will ...
2
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2answers
129 views

$E[F_T] = F_0 \ \rightarrow \ \text{or} \ \leftarrow \ p = \frac{1-d}{u-d}$?

From Ch 12 in Hull's OFOD, we compute the risk-neutral probabilities for a futures contract: Later in Ch 17, futures options are valued, and we have the same result: In relation to ...
2
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1answer
309 views

Why is this delta-hedging/P&L example on a variance swap call correct?

I'm looking into this article about var swaps: http://sbossu.com/docs/VarSwaps.pdf and not sure how to correctly interpret Exhibit 2.1.1. "In this example an option trader sold a 1-year call ...
2
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1answer
85 views

When $C(K_2) = C(K_1)$ for call options with the same expiration date

The exercise is to show $C(K_1) \geq C(K_2)$ where C(K) denotes the value of a call option on a stock price S with strike price K. We assume the expiry is the same for both. I have proved this by ...
2
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1answer
106 views

How literature come up with risk-neutrality problem, considering that market is not really risk-neutral?

I am searching on real-option pricing deficiencies to encounter risk-neutrality. As we know risk-neutrality assumption, is not hold in real situations. The problem is that I could not classified ...
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4answers
244 views

Is there any other way to measure option pricing model performance than proximity to market prices?

Short version Why do we take market prices as the prices to be estimated and predicted? The common answer is efficient markets hypothesis as in "Market agents do their best effort given their ...
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3answers
239 views

What noun is used to describe whether an option is call or put?

I'm not sure if this should be asked elsewhere, but it seems like a good place as any. Options have a strike price, they have an underlying instrument, and they have an expiry. They are also either ...
2
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1answer
273 views

Call option on a Mutual Fund

I am trying to price a call option on a mutual fund. Given the lack of market implied data, I am going to estimate the fund´s expected volatility using as a reference its historical volatility (...
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3answers
226 views

Why are short expiries associated with more pronounced volatility skews?

I've noticed that for a given strike price, the shorter expiration dates of options have more pronounced volatilities why is that?
2
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1answer
1k views

How to replicate this option?

I have a question I am not sure how to approach: Suppose interest rates is 50%, a stock worth \$1 today can be worth \$2, \$1, \$0.5 next year. If the option that pays \$1 only when S = \$2 is ...
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2answers
248 views

What is most reasonable approach to determine side of a multi-leg options order?

Say, 4-legged multi-leg options order with below leg ...
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2answers
498 views

Hedging credit risk using Put equity options

I am looking for some paper or similar which deal with this topic: hedging bankruptcy on firm's debt using Put options written on that firm's equity price. This should be based on the assumption that ...
2
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1answer
457 views

Calculating the probability of a price change using an options pricing formula

I don't know if I'm doing this right and I'd greatly appreciate help. I'm trying to use an option pricing formula to backout the likelihood of the Euro dropping below $1.27, even for a minute, at any ...
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2answers
251 views

Greeks and Option Premium

If a linear sum of options is constructed such that the premium payout is zero, then does it mean that resultant greeks of the cumulated options positions will be nearly zero. For simplicity, lets ...
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2answers
143 views

Buying one company or index against another, is this readily possible with options, with an accurate return (also Alpha Indexes)

There's a relatively new product in the market / on the Nasdaq called Alpha Indexes. It lets one own a company -- e.g. Apple, GE, Google, etc -- as the difference between how that company does (the "...
2
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1answer
69 views

Calculating probability of options with normal/lognormal distribution: does time make a difference?

I'm trying to calculate the probability of a calendar spread resulting in a profit at expiration, when estimating it is modeled as a lognormal distribution, by getting: ...
2
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1answer
90 views

Implied Volatility in Heston Model

recently I started reading the interesting book about option pricing in the stochastic volatility world from Lewis. He gives very interesting and detailed insights about this topic in general. However ...
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3answers
71 views

How would I exploit arbitrage if risk-neutral pricing doesn't hold? (Option Pricing)

We are just learning about binomial option pricing, and how the up-factor and the down-factor must match the risk-neutral price. p * u + (1 - p) * d = continuous risk free rate compounded CRR ...
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1answer
199 views

Feynman Kac Formula for path-dependent options

Consier geometric Brownian motion: $dS_t/S_t=\mu dt+\sigma dW_t$ Feynman Kac theorem tells us that the conditional expectation $v(t,x)=E[ e^{-rT}\Psi(S_T) | S_t=x]$ can be computed by solving the ...
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3answers
218 views

Why can't you arb skew by buying options with low implied vol and selling high implied vol in the same month and dynamically hedging?

there's something I've been trying to understand for a while now and I just can't quite understand with regards to skew. In the same month, why can't you buy a option that have low implied vol on the ...
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1answer
130 views

How to hedge a put under the Black-Scholes model?

To hedge a call, one would invest the option price proceeds into $\Delta_t*S_t + B_t = c_t$. (ok) However, a put has negative delta, so I would short $\Delta_t*S_t$ and invest $p_t+\Delta_t*S_t>...
2
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1answer
96 views

Pricing digital options in discrete time

I am stuck in this exercise from my textbook: Consider a one-period market model with $N+1$ assets: a bond, a stock and $N-1$ call options. The prices of the bond are $B_0=1$ and $B_1 = 1+r$, ...
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2answers
124 views

Braess's paradox in quantitative finance: When optionality leads to lower value…?

One of the standard tenets of quantitative finance is that options should have an intrinsic value because optionality as such (in the sense of having more choices) should bring about value. This ...
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3answers
430 views

Any New Discoveries in Quantitative Finance?

It seems like the field has become stagnant in the decades following the enormously successful and influential Black Scholes model. (The original paper has been cited a staggering 25,000 times - more ...
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1answer
247 views

Some questions about implied volatilities and how to generate theoretical prices when market prices are not available

I am building a little Excel file that take some option prices in input and plots the volatility smile/surface. I have a script that reads market prices from the option chain for 3 different ...
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2answers
468 views

How to compute the VaR for European Call, using the delta-normal method?

I have a European call option with current stock price $S_0$, strike $K$, risk-free rate $r$, volatility $\sigma$, and time to maturity $T$ years. I assume that the stock price at time $t$, which is ...
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1answer
1k views

Effect of time to maturity on european put option

Let $C(K,T,S_0)$ denote the price of an European call option with strike K and maturity T on underlying price $S_0$. Assume interest rate $r>0$. Then of course $C(K,T,S_0) \geq 0$ and $C(K,T,S_0) \...
2
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1answer
144 views

Asymptotic behavior of theta of vanilla call option

It is well known that the theta of call option is always negative. Also, the theta of (at the money call option) goes to infinity as the time approaches to the maturity. On the other hands, (ITM and ...
2
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1answer
736 views

How does Volatility Pairs Trading work?

I've read some material related to pairs trading for equities and I understand the process of finding non-stationary pairs price series that can be cointegrated to form a stationary series. The basic ...
2
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2answers
234 views

what is the actual point of vega on real option data

For a call option, we know that the vega is the derivative of the price wrt to the volatility. However the volatility, in that context, actually refers to the implied volatility of the specific call ...
2
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1answer
196 views

QuantLibXL - Optionlet bootstrapping failure

I am trying to bootstrap the Optionlet volatility surface from a Cap/Floor volatility surface using QuantLibXL. To be specific, the data is from ICAP: ...
2
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1answer
629 views

Implied probability density (Question 2 - Applications and Interpretation)

Using the second derivative of the Call-Option-Price one can try to recover the pricing density. Formally: Assuming a constant interst rate $r$ and also not making any assumptions on the model ...
2
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1answer
757 views

Aprox intraday implied volatility using intraday option prices and EOD greeks

I have two options datasets: EOD IV and Greeks Tick option and underlying prices I'm looking to calculate IV for each tick. Is there a way to approximate the ticks' IV using last EOD Greeks and IV?...
2
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1answer
152 views

Hedging differences between equity and index options?

Suppose we hedge an index option using futures on that index. How would the hedging strategy be different if the underlying could be traded directly (from a risk point of view)?
2
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1answer
167 views

OTC Equity Options' Dynamics

This only applies to options that do not have marketable equivalents since margin can be marked to them. I've never been able to find this on my goog. How is margin typically calculated for OTC ...
2
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2answers
2k views

How to calculate Vomma of Black Scholes model

This source (PDF) gives the closed-form for vomma (or volga, i.e. the second derivative of price w.r.t. volatility) of the Black Scholes option pricing model as: $$S_{0}e^{-qT}\sqrt{T}\frac{1}{\sqrt{...
2
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1answer
464 views

Is there any evidence that an option delta approximates ITM expiry probability?

Several sources (online and offline) that discuss the delta of a listed vanilla option, state that its delta is a (guesstimate?) of the probability of said option expiring ITM (in the BSM framework). ...
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2answers
497 views

Why don't options traders use charts? Or do they?

Retail trading platforms typically offer equity charts but only instantaneous quotes on options. It seems like even a few minutes of historical data would be useful when entering an order. Are charts ...
2
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1answer
965 views

What exactly is the annualized forward premium?

A forward contract has a premium of $ 0$ because it is an obligation to buy or sell something in the future (hence there is more risk). Call and put options, on the other hand, have premiums of $C$ ...
2
votes
1answer
29 views

how to compute the risk free rate for a given maturity of an option contract?

i'm working on options with different maturities. I need to correspond a risk free rate for each maturity. What rate should i consider as risk free rate? thank you.
2
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1answer
56 views

Option pricing: Risk neutral probability calculation

Let $u=1.3$ $d=0.9$ $r=.05$ $S(0)=50, X = \text{strike} = 60$. Assume binomial model Why isn't the risk neutral probability found by solving the following for $p$: $$E[S(T)]=p65+(1-p)45=S(0)(1+r)^T=...
2
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1answer
77 views

Option analysis

Assume zero dividend and that the strike price for a European call option on a stock at a fixed maturity T and strike price K is given by C(K).Suppose that $C(K)=e^{-k}$ for all $K\geq 0$ ,then, I ...
2
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3answers
120 views

Greeks for binary option?

How to derive an analytic formula of greeks for binary option? We know a vanilla option can be constructed by an asset-or-nothing call and a cash-or-nothing call, does that help us? Wikipedia states ...
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2answers
120 views

what is exercise frontier in option pricing

What's exercise frontier in option pricing? It kept popping up but I was never fully introduced to the concept. Follow up question: And is the optimal exercise time the first time the option is in-...
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1answer
124 views

What should be the sign of greek letter $\rho$?

I'm reading the book Risk Management and Shareholders Value in Banking by Resti & Sironi. I quote a paragraph from the book (Chapter 5, appendix): The derivative of an option’s value with ...
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183 views

European call down and out option (geometric Brownian motion, Monte Carlo, Euler)

I need to estimate the expected value and the Greeks of an European call down and out option, assuming geometrical Brownian motion of the asset, with Monte Carlo simulation employing Euler ...
2
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2answers
153 views

VaR calculation methods of options

I am a little bit confused about VaR in Options and I need a clarification for. I collected the following formulas, can you suggest what is the best formula and explain me why, please?
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1answer
453 views

Using FX ATM/RR/BF Volatility to Estimate Smile

Suppose $S$ is some FX rate, EUR/USD say, and $\sigma_{S}(K,T)$ is the implied volatility for some option written on $S$, sourced from the surface $\sigma_{S}(\cdot,\cdot)$ (alternatively, consider ...
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1answer
86 views

Black Scholes Model and Dividends

My question can be summarised as such: Consider a portfolio. Say it has a price $\Pi = x$. Portfolio consists of a stock and a sequence of call options underlying on the stock. It has been announced ...